Inference Based on SVARs Identified with Sign and Zero Restrictions: Theory and Applications

In this paper, we develop algorithms to independently draw from a family of conjugate posterior distributions over the structural parameterization when sign and zero restrictions are used to identify SVARs. We call this family of conjugate posterior distributions normal-generalized-normal. Our algorithms draw from a conjugate uniform-normal-inverse-Wishart posterior over the orthogonal reduced-form parameterization and transform the draws into the structural parameterization; this transformation induces a normal-generalized-normal posterior distribution over the structural parameterization. The uniform-normal-inverse-Wishart posterior over the orthogonal reduced-form parameterization has been prominent after the work of Uhlig (2005). We use Beaudry, Nam, and Wang's (2011) work on the relevance of optimism shocks to show the dangers of using alternative approaches to implement sign and zero restrictions to identify SVARs like the penalty function approach. In particular, we analytically show that the penalty function approach adds restrictions to the ones described in the identification scheme.

JEL classification: C11, C32, E50

Key words: identification, sign restrictions, simulation

The authors thank Paul Beaudry, Andrew Mountford, Deokwoo Nam, and Jian Wang for sharing supplementary material with us and for helpful comments. They also thank Grátula Bedátula for her support and help. Without her, this paper would have been impossible. This paper has circulated under the title "Algorithm for Inference with Sign and Zero Restrictions." Juan F. Rubio-Ramírez also thanks the National Science Foundation, the Institute for Economic Analysis (IAE), the "Programa de Excelencia en Educación e Investigación" of the Bank of Spain, and the Spanish ministry of science and technology (Ref. ECO2011-30323-c03-01) for support. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of Philadelphia, or the Federal Reserve System. Any remaining errors are the authors’ responsibility.